Contents:
Regional and global changes in land use and land cover have emerged as major issues
within the domain of research addressing environmental change (Rayner et al. 1994:
13). One of the most heavily scrutinized land cover transformations has been tropical
deforestation owing to its implications for potential climate change, biodiversity loss
and sustainable use (Houghton 1994). While there exists a broad understanding of the
global trajectories of deforestation and their underlying causes (Turner et al.
1990), progress toward deriving spatially explicit predictions and projections of these
trajectories at sub-global scales remains limited.
Explanations given to deforestation and other types of land degradation tend to be
shaped by the scale at which the analysis is conducted (Blaikie and Brookfield 1987).
Global level cross-national studies have been generally successful in establishing
statistical correlations between deforestation and such macro-level variables as
population, government polices, world market prices, and asset distribution, but the
utility of such findings is limited to the extent that they 1) represent inter-regional
averages that may not apply on a case-by-case basis 2) are devoid of spatial articulation
and 3) offer little insight into how the macro-causes being investigated interact with the
proximate land use activities that constitute the immediate sources of forest loss. In
order to address these deficiencies and to capture the uniqueness of particular
cause-impact relationships in specific situations, there is a growing consensus that a
regional schemata of land use/cover change (LUCC) processes is needed, comprising a series
of comparative case study analysis’s from which the most critical direct and
mediating variables affecting local land use decision makers can be discerned and measured
(e.g. McNeil et al. 1994; Kummer and Turner 1994; IGBP-HDP 1995). Models
derived from a theoretical framework of micro-level choice allow investigation of how
various combinations of bio-physical and socio-economic variables converge to drive
operational sequences of land use evolution (e.g. timber extraction to
agriculture), thereby providing the basis needed for robust regional projections of change
(Stomph, Fresco, and van Keulen 1994). Ultimately, by coupling - or aggregating - the
situational detail extracted from sets of region-specific models, a foundation is formed
for projections of land transformations at higher spatial scales (IGBP-HDP 1995: 9;
Mertens and Lambin 1997: 145).
The proposed study contributes to this framework with an investigation of the
socio-economic dynamics of land use change in the Southern Yucatan Peninsular Region
(SYPR) of Mexico, theoretically and empirically linking these dynamics with observed
changes in land cover as provided by remotely sensed imagery. By quantitatively relating
the landscape pattern to the economic objectives and constraints of the region’s land
managers, predominately consisting of semi-subsistence farmers, the study aims to produce
an assessment that is comparable in both structure and content to other recent empirical
studies of deforestation in Latin America (e.g. Pfaff 1996; Nelson and Hellerstein
1995; Chomnitz and Gray 1995). Like these works, this study couples satellite imagery with
spatially articulated data collected from field studies of socio-economic and ecological
conditions. A random sample of land manager units (mostly households) will be surveyed to
obtain detailed information on their land use practices, with particular attention given
to identifying the decision-rules guiding their activities. By geo-referencing the plot of
each land manager using Geographic Positioning Systems (GPS), the "ground level"
exogenous observations associated with each plot will be spatially linked to the imagery
of land cover, the dependent variable. The ultimate goal of the empirical model is to
predict simultaneously when, why, and where human induced land use change occurs.
The theoretical framework underpinning empirical specification of the model will be
informed by the agricultural household and agrarian change literature. This literature
distinguishes between two types of behavior characterizing semi-subsistence farmers, each
of which will be separately treated in the modeling effort. The first approach assumes
that farmers operate in a context of fully functioning markets, which, it will be shown,
leads to the theoretical result that their production decisions are reached independently
of consumption and labor supply decisions, even when part of their output is
self-consumed. In this instance, the land use choice can be modeled based on a
specification of the farmer’s objective function strictly in terms of profit
maximization. While such an approach is justifiable in regions of market-integrated farm
systems, its applicability in contexts of imperfect-markets may be undercut by
institutional and structural constraints that preclude an optimizing allocation of
resources. The second model will therefore relax the assumption required for the assertion
of profit maximization, instead allowing for the linkage of the farmer’s consumption
and production objectives as these affect his land use choices.
Because land use change is fundamentally a spatial phenomena, an additional feature of
the modeling effort undertaken in this research is the explicit incorporation of space as
an explanatory variable in land use decision-making. A key element in this regard relates
to the interdependencies between aggregate patterns of land use and the individual choices
that give rise to these patterns. Where a given land use conversion is undertaken is
determined by the returns or utility generated by that use at that particular location,
and these returns, in turn, are largely determined by the existing spatial distribution of
surrounding land uses (Geoghegan and Bockstael 1996). While the linkages between the
spatial arrangement of land use and land use change are receiving increased attention
within the economics literature on the subject, few, if any, existing empirical studies
investigate these linkages using individual decision-maker data.
Empirical implementation of the models will be undertaken using two econometric
approaches. The first approach will adapt the general dynamic panel-data model of Heckman
(1981) by employing a multinomial logit specification to model the discreet choice among
competing land uses based on each of the two theoretical frameworks cited above. The
second model explored, termed a hazard or duration model, is experimental, with this study
counted among its first applications to land use modeling. To be discussed further below,
hazard models estimate the instantaneous probability of a transition between states - in
this case land use states - conditional on the duration of the initial state.
Growing concern over deforestation has elicited increased efforts to model the
exogenous drivers and associated land uses underlying forest clearance in recent years.
These models have been based on varying degrees of theoretical rigor, with explanations
sought in factors ranging from the international trade relationships that integrate the
world economy (e.g. developed country demand for developing country timber products), to
the macro-economic structural characteristics of the tropical countries themselves (e.g.
high debt burdens leading cash strapped countries to exploit their forest endowments), to
the internal socio-economic and political institutional structures and conditions that
interact to cause socially sub-optimal forest destruction (e.g. high land concentration,
insecure property rights and poverty). While there exists a large and growing body of
studies conducted against the backdrop of these themes, a review of some of the most
commonly modeled variables reveals considerable empirical discrepancies, both within and
across scales of analysis.
Population (or its density) has received a great deal of attention, and although a
number of efforts using cross-sectional data have obtained findings indicating a strong
influence of demographic pressures on deforestation (Allen and Barnes 1985; Palo et al.
1987; Lugo et al. 1981, Cropper and Griffiths 1994, Rudel 1989), region-specific studies
often fail to concur. Using data on Brazil, Wood et al. (1996) and Pfaff (1996)
find that the effect of population disappears with the inclusion of other variables, while
Kummer and Sham (1994), Angelsen and colleagues (1996) and Harrison (1991) present results
indicating a statistically insignificant impact of population density in the Philippines,
Tanzania, and Costa Rica, respectively. Didia (1995), using a country-level data set, also
finds an aggregate measure of population to be statistically insignificant, but obtains
significant and positive results when she replaces it with a measure of the labor force.
Like population, the positive effect of roads on deforestation also has received
broad-based support in the literature, but here, too, pockets of dissent exist. Panayotou
and Sungsuwan (1989) find that the elasticity of forest cover with respect to road density
in Thailand to be just -0.11, while Lombardini (1994) and Osgood (1994) both find
insignificant effects of roads in Thailand and Indonesia, respectively. Barbier and
colleagues (1993) find for Mexico that increased road density is actually associated with
decreased cultivation area (and, by association, increased forest), and, in a later study
of Mexico, Barbier and Burgess (1996) find no effect of road density. Chomnitz and Gray
(1995) and Nelson and Hellerstein (1995), by contrast, both obtain a strong positive
association between distance to road and deforestation in Belize and Mexico, respectively.
The findings relating to other macro and micro socio-economic factors are no more
conclusive. While Burgess (1991) and Capistrano (1994) find deforestation to be positively
correlated with levels of income per capita in a cross-section of poor countries, they
obtain opposite signed coefficients on proxies for external indebtedness. Deacon (1994)
and Rock (1996), also using cross-sectional data, find evidence of a negative relationship
between per capita income and deforestation. Turning to agricultural productivity, Shafik
(1994) finds an insignificant impact of this variable using global cross-national data,
contrasted by Southgate’s (1994) finding of a negative and significant coefficient on
a cross-section of Latin American countries. On the regional scale, Katila (1992)
generates a negative coefficient of agricultural productivity using data on Thailand,
while Reis and Guzman (1994) and Constantino and Ingram (1990) both obtain positive
coefficients using data on Brazil and Indonesia, respectively.
Some part of the conflicting findings cited above may be attributed to the lack of
consistency on the definition of deforestation used for hypothesis testing. Measurements
used in the above studies include the average annual rate of deforestation (Didia 1994),
total area deforested (Burgess 1991), absolute forest cover (Palo et al 1987), percent
forest cover (Constantino and Ingram 1990), and growth in area used for crops and
livestock raising (Southgate 1994). These differences are non-trivial since they have an
immediate bearing on how coefficient estimates are interpreted. Kummer and Sham (1994),
for example, criticize cross sectional analyses that use percent forest cover as the
dependent variable, arguing that this measure represents cumulative deforestation and, as
such, cannot be used to make statements about recent deforestation in studies based on
countries with varying lengths of deforestation histories. A further source of discrepancy
can be explained on the basis of the exogeneity of the variables modeled. This is
particularly true for population and road measures. Cross-country studies will generally
contain population levels that are more exogenous than region-specific studies, since at
regional levels population and deforestation are likely to be jointly determined by other
factors such is soil quality and infrastructure availability. Similarly, to the extent
that road construction is determined by existing economic activity or on the basis of
development schemes, roads cannot be considered an entirely exogenous driver of
deforestation.
A recent and emerging class of models - and the one under which this study falls -
seeks to improve understanding of deforestation processes by exploiting recent advances in
high resolution satellite imagery to model forest clearance in terms of its proximate
causes. Although these proximate causes are well-known and frequently cited - slash and
burn cultivation, the conversion of forested areas for cattle ranching, government
sponsored resettlement schemes, and the provision of infrastructure, among others - there
have been few attempts to investigate them quantitatively. Ground-breaking work in this
regard is provided by Pfaff, Chomnitz and Gray, and Nelson and Hellerstein, all of whom
base their empirical analyses on profit maximizing models of individual decision-making at
the level of the land-manager. While Pfaff’s analysis derives an expression for the
demand for cleared land to examine the effects of population (i.e. migration), government
development projects, soil quality, and road density on deforestation in the Amazon,
Chomnitz and Gray and Nelson and Hellerstein frame the analysis in terms of those factors
that affect the profitability of land in different uses, these being primarily soil
quality and distance to road measures. In addition to theoretically capturing the direct
linkage between land use and deforestation, a further distinction of all three models is
their use of georeferenced data and preliminary spatial econometric modeling. These
features provide the basis for moving beyond causal explanations and into spatially
explicit predictions and projections.
In conclusion, the literature reviewed here can be broadly divided into those studies
which examine the driving forces or distal causes of deforestation, and those studies
which are rooted in behavioral frameworks to examine the human activities directly
connected to forest clearance. Only one of the works cited above, Pfaff’s,
quantitatively begins to link these two levels of explanation by examining the
determinants of migration. Like the other micro level studies reviewed, however, the
realism of Pfaff’s model is potentially compromised by the assumption of
profit-maximizing behavior, with its attendant assumptions of complete output and factor
markets. In this regard, a recent compendium of economic models of deforestation compiled
by Kaimowitz and Angelsen (1997) indicates only a handful of works that seek to explore
the implications of subsistence behavior for deforestation processes ( Angelsen 1996;
Deininger and Minten 1996; Dvorak 1992).No existing study, however, tests the quantitative
implications of a subsistence-based theoretical framework using georeferenced data.
Remoteness and the absence of perceived opportunities for exploitation relegated the
SYPR to a largely peripheral position in Mexican economic life prior to the 1960s. Other
than a small-scale trade in chicle at the beginning of this century, the first commercial
penetration did not occur until the 1950s when selective logging operations began. The
scope of these operations was too limited to stimulate complementary economic activities,
however, and the access roads that followed were evidently inadequate to encourage
subsequent agricultural settlement on any significant scale. With the depletion of
tropical hardwoods in the following years, logging diminished significantly.
Beginning in the mid 1960s, the objective of promoting what Katzman (1975) has termed
‘export-propelled’ agricultural frontier expansion underpinned a series of
policy initiatives to integrate the SYPR into the national economy. With three-quarters of
Mexico’s territory comprising arid and semiarid climates, and with most of the prime
irrigation sites in these regions already having been developed, policy makers redirected
agricultural development efforts to the promotion of rain-fed agriculture in the
country’s tropical lowlands (Gates 1988: 299). As Sanderson (1986: 39, 243) has
suggested, the agricultural sector in Mexico during this era was an ‘adjunct of
industrialization’, functioning both as a provider of cheap food to urban areas and
as a buffer for labor not absorbed by industry. Being strategically situated between the
communities of Chetumal, a free port on the west coast, and Escarcega, a railroad stop
near the east coast linking Yucatan with northern Mexico, the SYPR undoubtedly seemed
ideal for the development of an agricultural frontier that could simultaneously provide
staple exports for the region’s urban centers as well as function as a ‘safety
valve’ for excess labor both within these centers and in surrounding rural areas.
The completion of highway 186 in 1967 instigated the first influx of large scale
agricultural settlement to the region. Linking the two entrepots of Chetumal and Escarcega
via a largely unexploited tropical expanse, the highway was part of an extensive
road-building project across the peninsula that was intended to integrate the peasant
economy with local urban centers (Ewell and Merrill-Sands 1987: 111). Whatever the
expectations may have been with regard to the SYPR’s ability to complement the
Yucatan’s urban/industrial sector as a supplier of staples, the initial infusion of
settlers comprised mostly subsistence farmers, and their settlement along the highway may
have had less to do with its linkage to markets than with its role in affording subsidized
access to farmland given a lack of opportunities elsewhere. While the government
generously extended usufruct land grants in the form of collectively managed ejidos, as
sanctioned by Article 27 of the Mexican constitution, it initially did little to ensure
that ejido members (ejidatarios) had access to the capital necessary to produce
beyond subsistence needs. With land cheap and productive potential limited, most of the
agriculture in the region was practiced on an extensive basis, using traditional slash and
burn techniques (Boserup 1965).
The following two decades witnessed a barrage of government interventions that went
beyond simple land distribution to modernize peasant agriculture and accelerate the
transition from a subsistence to a commercial economy. These efforts were motivated by
lagging productivity in the ejido sector and a shortfall of basic foods nationally. At the
local level, the territory of Quintana Roo, in its quest to gain independent statehood,
declared an eight year long tax-free zone in 1972 to promote development of the region and
expedite its integration into the Mexican economy (Sierra et al. 1992). Federal policies
augmented these efforts. In the early 1970s, the parastatal marketing agency CONSAUPO set
guarantee prices for basic staples, principally maize, as an incentive for market
participation. In addition, a variety of federal agencies expanded programs to provide
bank credit, high-yielding seeds, fertilizers, agrochemicals, farm machinery, and
infrastructure to hasten the adoption of modernized agricultural techniques (Gates 1988:
297). While these interventions were a major driver of sustained colonization of the
region, their effect in reorienting farmer production strategies toward the market was
limited.
Rural development efforts were revitalized at the opening of the 1980s and were
bankrolled on oil reserves discovered in 1977, along with heavy foreign borrowing. Under
the auspices of the so-called SAM (Sistema Alimentario Mexicano), a massive and
comprehensive system of subsidies and credits was implemented to promote the production of
staples and thereby relieve an increasing dependency on food imports. In the SYPR, one of
the most visible impacts of the inflow of petro-dollars and the concurrent strategy to
increase food production was the start-up of wet-rice projects in the seasonally inundated
wetlands, or bajos, interspersed throughout the region. Sponsored by the government
and various non-governmental organizations, these projects were fully commercialized
ventures that required local participants to become financial stakeholders by borrowing
funds. The life span of these schemes was short-lived, however, and the majority collapsed
within a few years due to inadequate water control. In 1982, the SAM was rapidly
dismantled as the national treasury came under increasing pressure from falling
international prices for petroleum, massive foreign debt, successive devaluations of the
peso, and austerity measures imposed through an agreement with the IMF (Grindle 1984: 51).
By the mid 1980s, a radical revision of economic policies toward greater liberalization
was underway that would be bolstered by legal reforms beginning in the following decade.
In 1986 Mexico entered into the General Agreement on Tariffs and Trade (GATT), the impact
of which reached the agricultural sector by 1990, when tariffs on most products were
dropped or drastically lowered, subsidies on inputs were withdrawn or sharply reduced, and
the guarantee price was eliminated for all crops but maize and beans (Foley 1995: 62). The
continuation of these reforms was secured under the terms of NAFTA, effective in 1994,
obligating Mexico to fully liberalize its agriculture, including maize and beans, over a
fifteen year period. On the legal front, Article 27 of the constitution, which had served
as the embodiment of the government’s commitment to the rural poor since the end of
the Mexican Revolution in 1917, was amended in 1992 to 1) permit lands formerly held in
usufruct under the ejido system to be bought and sold, 2) open the possibility for joint
ventures between ejidos and private interests, and 3) terminate the continued distribution
of land to peasant communities. It was anticipated that these revisions would, in the
words of President Salinas (1992), both "capitalize the countryside and open
productive options" by establishing a legal framework guaranteeing property
ownership.
The pattern of land use in the SYPR had changed in a number of significant ways between
the closing years of the 1970s and the beginning of the 1990s. For starters, the wet rice
projects left an indelible imprint on the landscape. Because mechanical means had been
used to clear the bajo forests, secondary growth of vegetation was sparse once rice
cultivation was abandoned, leaving the affected bajos suitable only for cattle grazing
during the dry months. The destructive outcome of these projects as well as the rapid pace
of deforestation along the highway led the government to establish the Calakmul Biosphere
Reserve in 1989, located in the center of the study region. Roughly 50% of the
reserve’s 723,185 ha is ejidal property, 48% is government managed, and the remaining
2% is private. Production on the ejidos is primarily appropriated by the farmers
themselves, and is divided between subsistence crops (maize, beans and squash) and cattle
raising, though farmers also engage to a limited degree in the production of commercial
crops, including squash, and chiles.
As of 1995, the land certification and titling program that provides ejidatarios with
documentation of land ownership was still underway, so it is still too early to assess the
full impacts of the land reform. Preliminary reports from Mexican colleagues in the field
suggest that there is some hesitancy to privatize due to the fear of greater government
intervention via tax policies. In addition, a notable, if not tentative, observation is
that livestock production seems to be on the increase, apparently undertaken by ejido
members.
As semi-subsistence farmers, the SYPR’s ejidatarios belong to a class of economic
agents that is repeatedly implicated as a primary driver of tropical deforestation in
developing countries (e.g. Myers 1991; Houghton 1994; Consultative Group on
International Agricultural Research 1996). Progress toward theoretically linking the
economic discretion of these farmers to the implications for land use change, however,
remains limited. The development literature addressing subsistence agriculture has long
recognized that agricultural households combine two fundamental units of microeconomic
analysis - the household and the farm (Ahn et al. 1981: 520). This recognition has
stimulated the development of models which, in contrast to the traditional practice of
analyzing production and consumption decisions separately, explicitly incorporate the
interdependency of these decisions as they affect the allocation of resources (e.g.
Wharton (ed) 1969; Singh, Squire, and Strauss (eds) 1986). A major focus of these models
has been to explain the response of marketed supply to changes in prices and other
exogenous variables, with the linkages between this response and landscape patterns
remaining largely implicit. Nevertheless, they offer a potentially powerful tool for
addressing the choice among competing land uses that has yet to be fully exploited by
modelers of deforestation processes.
There are two criteria that have served as reference points for describing the
economics of farm household behavior: one is the proportion of total output consumed or,
alternatively, sold on the market, and the other is the proportion of family labor to
total labor input in production (Nakajima 1969: 165). At one extreme of this two
dimensional conceptualization are purely subsistence farms that consume only what they
produce and rely exclusively on their own labor. Because these farms do not engage in
trade, their production decision is immediately tied to the household’s consumption
requirements, and therefore must be modeled in an integrated framework. At the other
extreme are fully commercialized farms that sell all their outputs and purchase all their
inputs via market transactions. For these farms, the production problem is completely
divorced from the consumption decision and can be captured using a profit maximizing
formulation. The majority of farms in the developing world fall somewhere along the
continuum between these two extremes: food produced in excess of household consumption may
be sold on the market and the family labor force may be augmented by wage labor. In such
cases, there is no immediate theoretical justification for treating the household’s
production problem in isolation from consumption considerations (Sadoulet and de Janvry
1996: 140). Only under certain restrictive conditions, discussed below, does this
analytical division hold. Otherwise, as in the case of purely subsistence households, the
production and consumption problems must be treated as interdependent.
The construction of agricultural household models started in the 1920s with the work of
Chayanov, who, recognizing this interdependency, sought a theory of the peasant economy as
a mode of production distinct from that of the commercialized farm. Specifically, Chayanov
argued that the peasant household reaches its production and labor supply decision solely
on the basis of the consumption requirements of the family unit, whereby the age
composition of the household - or the ratio of consumers to workers - defines the maximum
level of effort willingly exerted by the workers to support themselves and their
dependents. Founded on his observations of the Russian peasantry in the 1920s, these
assertions could account for why the family would increase its labor effort in response to
unfavorable shifts in its terms of trade and decrease its effort in response to favorable
shifts, behaviors inconsistent with strict profit maximization. Similar views of peasant
behavior were embodied in the ‘substantivist’ school in economic anthropology (e.g.
Polanyi 1944; Dalton 1961), which rejected the use of formal economic analysis grounded in
optimizing behavior in favor of culturally-based interpretations (de Janvry et al.
1991: 1400). Like Chayanov, substantivists believed that most peasants live in an economy
in which group interests override individual interests. Accordingly, they argued that
decisions regarding the allocation of scarce resources are founded less on a rationality
of individual gain than on cultural norms, such as those involving reciprocity, kinship,
and tradition.
More recent theorizing has been dominated by neo-classical approaches, fundamentally
distinguishing themselves from the Chaynovian and substantivist schools by denying any
economically relevant distinction between commercial and peasant economic rationality. A
seminal formulation of this position is advanced in Schultz’s book, Transforming
Traditional Agriculture (1964), in which he develops and finds empirical support for
his celebrated ‘efficient but poor hypothesis’. In brief, this hypothesis posits
that peasant farmers make the optimum use of the resources at their disposal given the
constraints of their environment. Whereas the Chayanov and substantivist frameworks allow
for inequalities between costs and benefits at the margin, Schultz maintains that
subsistence farmers adhere to strict principles of allocative efficiency, and that any
gains in output can come about only through technical change rather than a reallocation of
resources. Along with Becker’s (1965) work on the process of time allocation within
the household when family labor has a positive opportunity cost, Schultz’s
contribution reoriented theoretical views about subsistence farms in developing countries,
and provided the foundation for the formalization of the neo-classical agricultural
household model.
This study proposes to explore the empirical implications of two distinct
specifications of this model for the land use decision. While each specification
postulates utility maximization as a basis for analyzing the optimal choices of the
household’s production and consumption decisions, they differ with regard to whether
these decisions are determined simultaneously. The first model proposed, termed a
recursive - or separable - model, postulates a deterministic, perfectly competitive
environment with a complete set of markets. These conditions allow the model to sever the
line of causation running from the household’s consumption to its production choice.
In this case, the production problem can be solved by profit maximization, with the demand
side of the model subsequently determined given the level of profit achieved. Consumption,
being determined ex post, thus has no bearing on the land use choice, which is
determined ex ante in the production problem.
Such an approach is susceptible to a number of criticisms, many of which were first
raised by Lipton (1968) in a cogent rebuttal of Schultz’s ‘efficient but
poor’ hypothesis. Specifically, Lipton cites imperfect markets for output, capital,
and insurance, compounded by climatic uncertainty and cultural restraints, as being
factors that preclude the peasant from allocating resources in a manner consistent with
marginal value product equalization. Farmers producing at or near the subsistence level,
he asserts, seek ‘survival algorithms’, not maximizing ones, and would choose
low value but robust crops that can be both consumed and marketed over higher-value,
climate-sensitive commercialized crops that require untested technological innovations.
Lipton’s argument undercuts the applicability of the recursive model in contexts
where fulfillment of subsistence requirements is at issue. In such cases, consumption
considerations have an immediate bearing on the production problem. The second model will
therefore explore the consequences of various market imperfections that result in the
break-down of the recursive property. Two such classes of market imperfections, and their
implications for land use, are discussed below: those in the labor market and those in the
insurance market under risk averse preferences.
Ultimately, the implications of assuming the separability condition will be manifested
both in the exogenous variables theoretically supported to determine the land use choice
and in the technique applied for empirical estimation. If it is assumed separability does
hold, the problem is greatly simplified, since no consideration need be taken of the
household’s consumption problem. In this case, the relevant variables would be
limited to those determining the profitability of the land in different uses, including
the market prices of the plot’s output and inputs, related policy variables (e.g.
price supports and government administered credit extensions and technical support), and
site specific factors such as measures of soil quality. If, on the other hand, the
separability assumption is deemed too restrictive, a more complex specification of the
land use problem is merited. Such a specification would likely require simultaneous
estimation of the household’s production and consumption choices., and, in addition
to the above variables, would incorporate variables such as family size and age
composition, attitudes toward risk, the availability of consumption smoothing devices such
as storage facilities, and the allocation of family labor between market employment and
household tasks.
The Recursive Model
The full version of the recursive model was developed by Barnum and Squire (1979) and
is based on the following assumptions: 1) The household unit maximizes a utility function
consisting of three arguments: an agricultural staple, a market purchased good, and
leisure. 2) The utility function is identical for each member and additive across
individuals. 3) The household faces exogenously given prices for factors and outputs. 4)
Family labor and hired labor are perfect substitutes. 5) Land is in fixed supply. 6) Fully
functioning markets exist for all factors and products. If, under these assumptions, the
utility function is maximized subject to a cash income constraint, a total time constraint
of family labor, and a technological constraint, it can be shown that the optimal
household production is determined independently of leisure and consumption choices. The
intuition behind this result is illustrated by the positive effect of income in
contributing to total household utility. Since income is a function of exogenously given
prices for output and labor, the household will attempt to maximize its net income in
accordance with the principle of marginal value product equalization, just as would a
profit maximizing firm. That is, the household will supply its product to the market until
the point at which the marginal costs of production equals the price it receives, and it
will demand labor so as to equate the marginal revenue product to the wage. Whether the
household is a net buyer or seller of labor or output has no effect on this result, since,
as a price taker, its valuation for both is determined exogenously.
This point can be illustrated by deriving the household’s demand for labor (see
Singh, Squire, and Strauss 1986: 17-20 for a complete solution to the model). Assume the
household maximizes the following utility function:
Max U=U(Xa, Xm, Xl)
subject to:
pmXm + paXa + wXl = w(Xl
+F) + paQ(L, A) -wL
where Xa, Xm, and Xl are the quantities of the
agricultural staple, the market purchased good, and leisure, respectively, pi
is the corresponding price of the commodities, w is the wage rate or cost of leisure, Q( )
is the production function for the staple, L is total labor input, F is family labor
input, and A is the fixed quantity of land. The constraint is derived by collapsing the
family’s income, time, and technological constraints into a single equation. The left
hand side of the constraint shows the total household expenditure on the market purchased
commodity as well as the opportunity costs associated with consuming its own output and
time in the form of leisure. The right hand side represents the household’s full
income, comprising total family time (valued at the market wage) and profits. Maximizing
the utility function with respect to the choice variable labor (L) obtains:
pa
Q/
L = w
indicating that the household will equate the marginal revenue product of labor to the
market wage. Moreover, the absence of Xl, Xa, and Xm from
the above equation shows that the household’s utility function has no bearing on the
total labor input decision. Use of this factor is thus consistent with profit maximization
and is independent of consumption choices.
The consumption side of the model is, however, dependent on production. This is because
the household behaves as if its consumption decisions are made on the basis of prices and
income, the latter of which is determined by the solution to the profit maximization
problem. Specifically, it can be shown that the effect of an increase in the price of the
agricultural staple can be decomposed into two components, a substitution effect and a
profit effect:
dXa/dpa = 
Xa/
pa + 
Xa/
Y* *
Y*/
pa
The first term on the right hand side of the above equation is unambiguously negative
for a normal good; as a consumer of the staple, the farmer responds to an increase in its
price by decreasing demand. The second term captures the farmer’s response as a
producer of the staple. It shows the effect of an increase in the profit maximizing
income, Y*, via an increase in the price of the staple, pa, on the
amount of the staple demanded. Since this term is unambiguously positive for a normal
good, the net effect on the quantity demanded from a price increase is indeterminate and
depends on the income elasticity of food consumption. The presence of Y* in the
above equation is evidence of the model’s recursive property; with prices exogenously
given, the consumption decision is seen to be related to the production decision through
the level of income obtained from profit maximization.
Non-recursive (non-separable) models
Recursive models are applicable whenever prices are exogenous and markets are used,
even if there are significant transaction costs involved in purchasing or selling the good
in question. Their theoretical validity is compromised, however, when these transaction
costs become so high as to induce the farmer to choose self-sufficiency over market
participation. A depiction of this circumstance is given in Figure 1. Farmers in
underdeveloped regions typically face a wide band between the low price at which they
could sell a commodity or factor and the high price at which they could buy that product
or factor, as indicated by the two price curves Pbuy and Psell in
the graph. Factors that increase the magnitude of the band include high transportation
costs, shallow local markets, and price and/or quantity risks coupled with risk aversion
that cause the certainty equivalent price and farm gate price to diverge. A market failure
occurs when the household is constrained to equate its own production with its own
consumption for some commodity(ies), that is, when the subjective value (i.e. shadow
price) that the household attaches to the relevant good falls within the price band. In
this instance, the production decision is based on the equilibrium of supply and demand
given by an ‘in-house’ market for the good. Since prices are no longer taken
parametrically, but rather are determined by the household’s choices, production of
this non-traded good is directly linked to its consumption. Market participation - and the
severance of this link - occurs when the shadow price falls either above or below the
price band: if above the upper limit (i.e. above the market purchase price), the household
will enter the market as a buyer, and conversely, a shadow price below the lower limit
defines the household’s market participation as a seller.
Non-separability affects farm household modeling in two ways: theoretically, it changes
the comparative statics and empirically, it renders statistically inconsistent the usual
demand and supply parameter estimates (Singh, Squire, and Strauss 1986: 48). Both of these
affects follow from the replacement of exogenously given market prices with endogenously
derived shadow prices, which are a function of both household specific preferences and
technology. How non-separability impacts the choice of land use depends on the source of
the market failure and the goods or factors that are effected by it. Labor market
imperfections, for example, may influence land use by limiting the number of crops that
can be grown by the household, or, given a surplus of family labor, by inducing farmers to
cultivate their land more extensively in response to insufficient off-farm employment
opportunities (Benjamin 1992: 315). Alternatively, missing markets for insurance may lead
risk-averse farmers to allocate a greater share of their land to a staple crop despite
greater expected profitability of cash crop production (e.g. Hammer 1986). A
priori it is difficult to assess which, if any, imperfect markets characterize the
economy of the SYPR, but each of these examples is anticipated to be of relevance. A brief
review of the literature addressing labor and insurance market failure will therefore
serve to indicate some possible approaches to modeling the land use decision.
Missing insurance markets
An empirically well-established assertion of farmers in developing countries is that
they tend to be highly risk averse, preferring lower but certain levels of income to
marginally higher uncertain income levels ( Moscardi and de Janvry 1977; Dillon and
Scandizzo 1978; Binswanger 1980; Walker and Ryan 1990). Risk aversion drives a wedge
between the certainty equivalent price, which is used for decision making, and the
expected price, which is discounted by a mark-up that reflects the level of risk and
degree of risk aversion. With sales prices discounted negatively to hedge against risk,
and purchase prices discounted positively for the same reason, a price band is created
which opens the possibility of market failure and the violation of the separability
condition (Sadoulet and de Janvry 1995: 150).
Roe and Graham-Tomasi (1986) examine the implications of risk aversion for separability
by incorporating production risk into a dynamic agricultural household model. They
demonstrate that, unless onerous assumptions are imposed on the preference structure of
the household, the separable model does not survive in a context in which yields are risky
and insurance markets are absent. The underlying intuition behind this result is that risk
aversion in consumption induces risk aversion where profits are concerned. After
specifying a Cobb-Douglas production function which incorporates risk multiplicatively, in
addition to an additively separable, time invariant utility function that includes
arguments for consumption, leisure, and an intertemporal financial asset, the authors show
that the first order conditions for expected utility maximization are identical to those
of a firm maximizing expected utility of profits. The distinguishing trait of these first
order conditions, however, is that they contain the levels of optimal commodity
consumption, which are unknown, therefore implying that input choices do depend, in
general, upon consumption bundles. Based on their theoretical findings, they warn that
empirical estimates generated from models that erroneously ignore risk will be biased
upwards with regard to the quantity of output and resources allocated to production, and
biased downward with regard to the resources allocated to off-farm activities.
Saha (1994) obtains similar findings by moving beyond Roe and Graham-Tomasi’s
analysis to include both output and price risk in the household’s decision
environment. Like these authors, he assumes that there are complete product and factor
markets, but missing markets for insurance. His paper focuses specifically on the
household’s short-term risk response in a two season framework, where the seasons
correspond to the times of harvest and planting. The model is set up in two parts. In the
harvesting season, the household maximizes utility with respect to consumption, the sum of
on and off-farm family labor (i.e. leisure), and the amount of the harvest sold or placed
in storage for sale or consumption in the subsequent planting season. These decisions are
made under price risk, since prices in the planting season are unknown. Once the planting
season arrives, the choice variables become consumption, the sum of on and off-farm family
labor, and the sum of family and hired labor in on-farm production. These decisions are
made under quantity risk, since the farmer does not know based on his or her current
choices what the realized output in the harvesting season will be. The first order
conditions corresponding to both seasons indicate that the optimal level of choice
variables can be determined only by solving each system of equations simultaneously;
hence, separability does not hold. Empirical estimation of the model using production,
consumption, and price data from a village in India, reveals that the parameters measuring
risk aversion do, in general, have a statistically significant effect on the
household’s optimal responses. In particular, the results show that the optimal
consumption response to higher riskiness of price or output is negative and significant,
and that on the production side, one means by which the household attempts to mitigate
risk is by increasing its off-farm labor supply.
Three ingredients which are common to the approaches taken by Roe and Graham-Tomasi and
Saha in theoretically demonstrating the non-separable result under risk are worth noting.
The first - standard in the literature on LDC agriculture - is the assumption that farmers
are risk averse. Second, farmers have no access to contingent claims markets, but third,
they do have means internal to the household for mitigating risk via the presence of
decision variables that can be used to smooth consumption over time. In Roe and
Graham-Tomasi’s analysis, this consumption smoothing device is captured by the
household’s holdings of a financial asset, whose value is equal to the difference
between its income and consumption in the previous period. A corresponding role is played
by the storage variable in Saha’s framework, which serves to link household
consumption over the two seasons. The presence of such intertemporal variables is
important since they are one mechanism by which the farmer shifts the burden of adjustment
to external shocks, and ultimately help to account for the farmer’s sluggish response
with respect to the other choice variables, including output and factor use.
Neither of the above analyses focuses in depth on land as a production factor, or at
issues relating to the farmer’s choice-mix between food and non-food crops as a way
of dealing with risk. Nevertheless, two interesting hypotheses emerge with respect to land
use from their results. The first is given by the potential role of Roe and
Graham-Tomasi’s financial asset in influencing choices made between subsistence and
commercial land use techniques. In particular, incorporating financial assets opens a
possible avenue for exploring the effects of family remittances in decision-making, a
factor which a number of authors have identified to be important within Mexican farm
households (e.g. Grindle 1989; de Janvry et al. 1996). In this regard, it
might be hypothesized that those families with a greater stock of wealth are likelier to
engage in riskier but more profitable commercialized farming activities, given the
existence of a fall-back in cases of crop failure or adverse market fluctuations.
Likewise, Saha’s stock variable could play a role similar to an asset by providing a
carry-over buffer that relaxes the farmer’s constraint of meeting subsistence
requirements. Hence, all else equal, acreage in commercial as opposed to subsistence crops
could be hypothesized to be greater for those farms with access to storage facilities.
Assessing the relevancy of these issues for the SYPR is an empirical matter which will
receive close scrutiny during the field studies.
An additional modeling consideration that may cross-cut the issues of risk and
separability relates to the dual set of property rights that exist under the ejido land
tenure regime. Ejidatarios have rights of access to both individually and collectively
managed lands, with the latter comprising almost three-quarters of all ejido land in
Mexico (Thompson and Wilson 1994: 449). Access to such lands opens at least two
potentially important avenues for ejidatarios to hedge against risk: through spatial
diversification of crop production and through animal husbandry. The former option is
viable only if there is significant heterogeneity in biological and meteorological
conditions within relatively small areas. In this instance, farmers may acquire a
portfolio of parcels across which yield risks are not perfectly correlated (Walker and
Jodha 1985: 25), thereby insuring themselves against localized adverse events such as
pests and droughts. An alternative insurance may be derived from cattle ownership. Not
only can cattle can survive from vegetation produced by rains that are insufficient for
crop production, but they can also be easily shifted to different locations depending on
climatic conditions (Binswanger and McInire 1987: 75). Whether or not the common
property/usufruct dichotomy merits explicit incorporation as a discreet choice variable in
the individual ejidatario’s land use calculus will depend on a number of factors,
including the specifics of the rules governing access to common property and the degree to
which decisions regarding the use of such property are reached communally.
Imperfect labor markets
An alternative angle from which to approach the issue of non-separability is via
investigation of rural labor markets. The question of whether agricultural households are
price-taking participants in a clearing labor market dates back to the research of
Chayanov, who argued that such a condition only exists within capitalist farm systems
where there is a clear division between labor and the owners of capital. Since the
material wants of the family farm that Chayanov theorizes are strictly defined by the
family’s consumption requirements, even the existence of relatively lucrative
alternative employment opportunities are not sufficient to entice a household laborer off
the farm. ‘Wages’ are thus determined endogenously as a function of an
exogenously given family labor supply, implying non-separability of the household’s
production and consumption choices. Chayanov’s underlying premises are clearly open
to considerable scrutiny on neo-classical grounds (e.g. Millar 1970), but recent
scholarship has arrived at his result of an endogenously determined value of labor while
adhering to the paradigms of marginalist analysis. This scholarship has proceeded from the
assertion that imperfect substitutability exists between on- and off-farm labor.
Lopez, for example, argues that production, consumption and labor supply decisions may
be interdependent because of differences in the preferences for off-farm and on-farm work
or because of the costs of commuting associated with off-farm work. He develops two
models, one corresponding to each case. In the first model, the household’s utility
function is given by U=U(H-L1, H-L2, X), where H is the
household’s total time endowment, L1 and L2 are the supplies of
the households on and off-farm labor, and X is a consumption good. Maximizing this
function subject to a time and budget constraint, which includes an implicit specification
of the farm production function, yields a system in which utility and profit maximizing
decisions are jointly determined. The second model discards the assumption that
preferences vary across types of labor, and instead inserts a variable t accounting
for the travel time involved in off-farm work: U=U(H-L1-L2-t,
X). This form, however, ultimately reduces to the one given in the first model, except for
the inclusion of an additional parameter in the utility function measuring the value of
the travel time variable. Thus, Lopez demonstrates that even when the household’s
preferences for off and on farm work are identical, it behaves as if they were different
when travel costs are involved. In the empirical implementation of the model on Canadian
census division farm data, he uses standard nonnested hypothesis techniques to compare
separating and non-separating models. After simultaneously estimating a set of
commodity/leisure demand equations, a conditional profit function, and output supply and
factor demands, he finds statistical evidence in favor of rejecting the recursive model.
Contrary evidence of this result is provided by Benjamin (1992), who, like Lopez, is
concerned with modeling the implications of various structural constraints on labor
mobility across on and off-farm work. Benjamin investigates three conditions that
theoretically result in separability: a binding constraint on off-farm employment, as may
characterize the slack season; rationing on the labor demand side, conversely
characteristic of the peak season; and differing returns to on and off-farm employment, as
in Lopez’s approach. Of particular interest is Benjamin’s empirical methodology.
In contrast to the approaches reviewed above, which simultaneously estimate the producer
and consumer sides of the model due to the presence of unobserved implicit prices,
Benjamin estimates the fully reduced form of the model, excluding these prices. The
drawback of this procedure is that none of the original parameters and hence constraints
they are supposed to satisfy can be identified (Sadoulet and de Janvry 1995: 160). If the
concern is exclusively on testing for separability, however, its advantage is that any
flexible form of estimating the dependent variable can be chosen. Opting for a logarithmic
specification, Benjamin runs a series of regressions on factor use, with their
distinguishing characteristic being the inclusion of the household’s demographic
traits as explanatory variables. He tests the null hypothesis of separability by testing
whether the parameters of the demographic variables are jointly significantly different
from zero in the production equations. Applying the model to cross sectional rural
Javanese data, Benjamin consistently fails to reject the null, including in regressions of
labor demand and area harvested.
Because market failures are generally household specific rather than good or factor
specific, one weakness of the above two empirical investigations of labor market
imperfections is their failure to filter the data sets according to the extent of market
participation by household. This means that the empirical results obtained represent an
average across a sample of households which may exercise highly varying degrees of market
integration, thus potentially biasing the results in favor of rejecting the significance
of demographic variables. Since the hypothesis of non-separability applies only to those
households that do not participate in the market, ideally its testing should be carried
out on data sets containing only such households.
In an investigation of rural labor markets in Mexico, Sadoulet, de Janvry and Benjamin
(1996) address this issue by developing a methodology by which household membership to
market integrated and self-sufficient labor regimes can be identified prior to testing of
the non-separability hypothesis. They begin with a theoretical model of utility
maximization which distinguishes between skilled and unskilled family farm labor and
between on and off-farm work. Farm assets, including labor stocks and land, and transfers,
as from family remittances, are assumed to be exogenously given. The household’s
utility function consists of three arguments: the leisure of its skilled and unskilled
members and income. After maximizing this function subject to a series of non-negativity
constraints on hired and family off- and on-farm labor, they derive an expression for the
shadow wage of family labor, which is shown to be positively related to farm assets and
transfers, negatively related to the stock of unskilled labor, and ambiguously related to
the stock of skilled labor. Based on this reduced form expression for the shadow wage,
they then estimate an ordered probit model which categorizes households according to
whether they are net sellers, net buyers, or self-sufficient in labor use. Threshold
values for each of these categories are the opportunity costs on the labor market for
sellers and buyers, and are estimated using household specific data on the transaction
costs of labor market participation. After categorizing their sample of observations into
the three labor regimes, the authors subsequently run three corresponding regressions of
labor intensity per unit of land on variables measuring the asset position of the
household and its labor productivity. To correct for selectivity bias, the Inverse Mills
ratio retrieved from the ordered probit is included in each of the regressions. They
obtain findings overwhelmingly supporting the hypothesis of non-separability: the
demographic and consumption variables are jointly significant only for those households
that are self-sufficient in labor, while for the net sellers and net buyers these
variables are insignificant.
Sadoulet and colleagues approach offers a means of fine-tuning the empirical model
according to the critical variables determining factor use for different land-manager
types. In their model, land is taken as fixed, and one possible extension is to endogenize
this variable and explore the implications for land use of differing stocks of wage and
farm labor across households. A possible refutable hypothesis in this regard is that those
farm families with relatively low stocks of skilled (marketable) labor or those facing
relatively high transaction costs to labor market participation use their land more
extensively due to the lack of alternative income generating opportunities.
The data
The data set used for this research will merge available satellite imagery with
household and government census data collected during the course of eleven months of field
work. Two sources of satellite data comprising seven images that span the period from 1975
to 1996 will be drawn upon. The primary source, Landsat Thematic Mapper (TM) data, is
available the years 1984, 1987, 1993 and 1996, while the secondary source, Landsat
Multispectral Scanner (MSS) data, is available the years 1975, 1985, and 1990. The
modeling exercise will rely predominately on the TM data because of its higher spatial and
spectral resolution, which provides for the identification of more detailed land classes.
It is also possible to combine the TM and MSS data, thereby expanding the temporal window
but at the cost of a more coarse classification scheme.
Since the ultimate goal of the model is to produce a set of conditional land use
transition probabilities, one of the first steps will be to identify the number of
distinct classes to be modeled. This choice will be determined both by the major trends in
land conversions during the period of observation and by the technical constraints of
accurately isolating land use classes from the imagery. A very broad classification might
distinguish between ranching, agriculture, and natural vegetation, while a more
disaggregate classification might further refine agricultural classes into maize-swidden,
rice cultivation and small scale plantations. In addition, it might be possible to
identify classes of natural vegetation according to their stage of growth. Such
refinements would modify the transition probabilities associated with the
modification/conversion of different types of land uses/covers, and would potentially
improve the precision of the model provided that distinct transition probabilities for
each of the sub-classes exist.
Data for the explanatory variables will collected on the basis of two surveys jointly
undertaken by Peter Klepeis, a doctoral candidate in Clark University’s Department of
Geography, Birgit Schmook, a research associate of ECOSUR-Unidad Chetumal, and this
writer. The first survey (see Appendix I) will elicit information collected at the
household level on consumption expenditures (market purchased and subsistence), labor
supply (broken down by sex and skill level), farm and non-farm outputs, purchased and
household supplied variable inputs, fixed farm assets, basic demographic characteristics,
and land use patterns. In addition, questions will be posed relating to the
household’s history in the area, such as when they arrived, how much land did they
initially have access to, were there significant changes in their agricultural activities
through time, etc. The second survey will be directed at the community leaders of each
ejido to obtain general information on the land use history of the ejido and on the rules
governing access to land within the ejido. Data collected from government archives and
census records will augment the surveys, and will include information on changes over time
of the macroeconomic environment, such as prices for consumption and production inputs,
interest rates, population growth, and government projects.
Modeling approaches
The model will employ a discreet choice probabalistic approach to estimate transition
probabilities across land uses conditioned on the features of the pixel of observation and
its surroundings. This approach considers that there is a continuous latent random
variable reflecting utility or net returns from pixel i in land use m at
time t, where returns could be influenced by such factors as the risk of a
particular land use, the market price of its output, or the contribution of its output to
the household’s subsistence requirements. In its general form, this index of utility
or returns, (Iimt) may be represented by a function of exogenous variables (Ximt)
and parameters (b mt) and an error structure (e imt):
Iimt = f(Ximt; b mt) + e imt for all m =
1,...,M
It is hypothesized that pixel i will be converted from use m to use k
at time t if:
Iikt > Iimt for all m ¹ k
Given that only the choice of land use, not the latent variable itself, is observable,
the objective is to estimate the probability that the utility from a particular land use k
is greater than under land use m for all m = 1...M. Referring to the
stochastic specification, if the e are Weibull distributed and uncorrelated across land
uses m, estimation of this probability is equivalent to the multinomial logit model
where
Prob (Iikt > Iimt) = exp(b iXk)
å m exp(b iXm)
The model could alternatively be specified as a multinomial probit if the errors were
assumed to come from a normal distribution.
The application of this style of model follows the works of Chomnitz and Gray (1995)
and Nelson and Hellerstein (1995) in their studies of deforestation in Belize and Mexico,
reviewed above. By positing profit maximization, these authors implicitly invoke the
assumption of separability and include among their exogenous variables only those factors
that affect the profitability of a given parcel in different uses. The starting point for
the empirical analysis in this paper, made possible by the collection of household level
data, is the relaxation of the separability assumption. While the particular specification
of the model awaits information gathered during the course of the survey work, its basic
distinction will be the inclusion of variables measuring the consumption side of the
household’s decision making, thereby forming the basis for testing of the
separability hypothesis. One possibility in this regard is the application of an F-test:
If the coefficients of the consumption variables are jointly insignificantly different
from zero, separability will fail to be rejected, and the final specification will include
only those variables relevant to the production decision.. Alternatively, if separability
is rejected, the final specification will include the variables measuring the
household’s consumption.
An alternative econometric modeling approach that will be explored is hazard or
duration models, which estimate the instantaneous probability of a transition between land
use states conditional on the duration of the initial land use state of a pixel. The first
step in this approach is to estimate the impact of a set of independent variables on a
dependent variable termed a spell, which in this application is the length of time a pixel
is in a given land use. Spells can either be measured in the temporal or spatial
dimension, thus permitting an investigation of land use dynamics from two angles. In the
temporal sense, a spell is the length of time that elapses from the beginning of a state
until a transition or until measurement is taken (Lancaster 1990). The spatial counterpart
is the Euclidean distance measured between events (Pellegrini and Reader 1996), where the
event is some distinguishing characteristic of the pixel, such as a specific technology
application or market orientation of an associated farm.
Mathematically, the hazard function is expressed as:
l (t) = lim P(t £ T < t + dt½ T ³ t)/dt
dt® 0
where T is the spell length and the condition T ³ t is the event that the state is
still occupied at time t. The issue of temporal conditionality can be illustrated with a
simple example given by Lancaster (1990: 7): the hazard l (45) gives, say, the proportion
of 45 year olds who die within dt after their 45th birthday, while the
unconditional concept gives the proportion of people ever born who die within dt after
their 45th birthday.
A common parametric specification of hazard models is that of the Weibull, given by:
l (t) = p*exp(xkb k)p tp-1
where x represents a vector of exogenous variables, known as covariates, the b ‘s
are estimated coefficients, which measure the impact of the independent variables on the
conditional probability of exit from the state, and p is a parameter indicating the
direction of duration dependence, that is, whether the conditional probability of exit is
an increasing or decreasing function of time. Generally, the inclusion of covariates,
which can either be static or time varying, has no relevance for the question of duration
dependence (Greene 1993: 721). Their impact is rather to shift the entire function upward
or downward by a constant percentage. One assumption necessary for the use of the Weibull
is a monotonically increasing or decreasing hazard function, alternatively stated, a
function with no sign shift in duration dependence. If statistical tests reveal this
assumption to be too restrictive (see Kiefer 1988: 661), semi- and nonparametric
specifications can be applied which allow for greater flexibility.
The implementation of a hazard model in this study will not be used to test the
theoretical propositions regarding recursivity discussed above. The inclusion of this
model instead serves an experimental investigation of a methodological device that can be
used for temporalizing the otherwise static range of analyses possible using time specific
satellite data.
Geographic parameters of the study region and sample design
The population under study resides within a 5,000 km2 swath spanning the
base of the Yucatan peninsula through the two Mexican states of Campeche and Quintana Roo.
Highway 186 passes through the center of the study zone and connects the ejidos of Nicolas
Bravo and Lago Silvituc, located on its eastern and western boundaries, respectively. The
northern boundary coincides with that of the Calakmul Biosphere reserve, while the
southern boundary extends within in a few miles of Mexico’s border with Guatemala.
Roughly 125 ejidos occupy the zone thus delimited. Aside from ranching operations, which
are commonly on private land, four principle land uses are represented within the ejidos:
milpa (subsistence oriented swidden agriculture), chile cultivation, failed rice projects
(many of which have been converted to pastures for livestock) and incipient orchards. Each
of these uses falls under one of two broad land cover classifications: bajo wetland or
upland environment.
Ideally, the sample design would ensure that the land managers associated with each of
these use/covers are represented in approximately the same proportions as their
representation within the entire population. A multistage cluster procedure will be
applied to approach this ideal, while at the same time accommodating the limitations of
the available sampling frames. Two primary tools will serve the design: the 1990
government censuses containing population figures for each of the ejidos and major
villages contained therein, and a map of the study region - currently under construction -
delimiting the highway, the boundary separating Campeche and Quintana Roo, the location of
the largest village within each of the ejidos, and a rough sketch of the ejido boundaries.
The first task is to divide the population, comprised of household units, into strata
based on their geographic location. Stratification provides a cost-effective means of
improving the representativeness of those variables on which it is based while
simultaneously maintaining the randomness of the sample. Geography is the logical choice
for stratification in this study because it is correlated with a number of other variables
that are likely to be important for land use (e.g. distance to road, soil quality,
climate, state regulations), thus indirectly improving their representativeness in the
sample. A total of eight strata are identified. Four of these are formed by the
intersection of the highway and the boundary between Quintana Roo and Campeche, dividing
the region along north-south and east-west axis. An additional four strata are formed by
considering those ejidos that border the highway on both its north and south sides within
each of the two states. Private property is an additional land use category which will
form its own separate strata. Currently, no sampling frame is available that lists the
privately held parcels in the region, though it is believed that their percentage is very
small. Despite its small number, however, this group could potentially be important for
land use change in the region. If information gathered in the field indicates this to be
the case, and if no records exist to permit the formation of a separate strata, then the
sample will be augmented to include representation of private parcels. Later, in the
empirical analysis, weighting procedures can be applied to adjust for their arbitrary
inclusion.
The second step is to individually select one ejido, and, by association, one village,
from within each of the eight strata on the basis of random sampling techniques. Selection
of the ejidos will proceed according to probabilities proportional to size. That is, each
ejido within a strata will have a chance of being selected proportional to the size of its
population. For example, if strata 4 has a total population of 100, 30 of which are
located in ejido A and 70 of which are located in ejido B, then ejido A is assigned a
30:100 chance of being selected while ejido B will have 70:100 chance. To carry out
selection, a three digit number ranging from 001 to 100 is randomly chosen. If this number
is from 001 to 030, ejido A is selected; if it is between 031 and 100, ejido B will be the
choice.
To determine the number of households from within each ejido to sample requires three
pieces of information: the total population of the study area (calculable from the
government census), the percent of the total population that is to be sampled (i.e. the
sampling fraction), and the selection probabilities applied in the first stage of
selecting the ejidos. Assume, for example, that the total population is 1000, that the
target sample size is 200 (yielding a sampling fraction of 1:5), and that ejido A was
randomly chosen from strata 4. To move from the first stage probabilities applied in
selecting ejido A to the overall sampling fraction of 1:5, a compensating selection rate
must be applied in selecting the households. Since ejido A had a probability of selection
of 1:3, maintaining the overall rate of 1:5 requires that households from ejido A be
sampled at a rate of 2:3. Thus, a total of 20 households would be represented from strata
4. Applying this technique to each of the other 7 strata would yield the target sample
size of 200, with each strata represented in the same proportion as its share of the total
population.
In the final stage, the survey respondents themselves will be chosen randomly from each
ejido after an inventory of households is created. A necessary step in this process is to
make contact with the comisariado (community leader) of each ejido, who is responsible for
keeping updated records of all residents. At this point, a judgment call will have to made
as to whether to limit the sample to a single village within the ejido. Most ejidos have a
‘primary’ village whose population is at least twice as great as the second
largest, and in many ejidos this village is the only population cluster. Based on
discussions with the comisariado and pending the specifics of the information contained in
his records, stratification procedures can be applied once again either across villages in
the ejido or just within the primary village. This decision will be based on an assessment
of the degree of intra-village homogeneity and the associated potential for high sampling
error. If, for example, the households within each village were virtually identical with
regard to a certain characteristic believed to be important for land use (e.g. income),
but completely different from the households in other villages of the ejido, the
additional time costs of sampling across villages would be clearly justified. By contrast,
if the variability within villages were roughly the same as the variability across
villages, then the costs of increased sampling error as a result of within-village
sampling would likely be compensated by the commensurate potential for obtaining a greater
sample size. Reality is likely to fall somewhere in the middle of these extremes, and the
trade-offs between sample size, depth of contact with respondents, and sampling error will
have to be carefully weighed.
The final sample is projected to comprise roughly 250 households distributed across
eight to twelve ejidos, in addition to a maximum of 20 households on privatized plots.
While a standardized questionnaire will be applied across the sample, approximately
one-third of the households will receive more intensive investigation based on in-depth,
open-ended interviewing techniques. Because this sub-set will comprise a comparative case
study analysis of land use histories by manager type, particular attention will be given
to the long-time residents of the region.
This study is a component of a larger multi-disciplinary research effort underway that
integrates remote sensing with ecological and socio-economic studies of land use/cover
change in the SYPR. Funded by NASA’s Land-Cover and Land-Use Change Program, the
larger project joins researchers from the George Perkins Marsh Institute (GPMI) of Clark
University, Harvard Forest, and ECOSUR-Unidad Chetumal in an effort to derive spatially
explicit, probability-based models of land conversion in the region. Each of these groups
will bring their specialized expertise to bear on the respective facets of the project:
spatially explicit classification of land cover for the entire region (GPMI); processing
and interpretation of ecological and bio-physical data (Harvard Forest); and local expert
interpretation of the ejido political economy, Maya agriculture and livestock production
(ECOSUR). The research pursued in this dissertation will depend critically on the inputs
provided by these groups.
Ahn, C. Y., I. Singh, and L. Squire. 1981. A Model of an Agricultural Household in a
Multi-Crop Economy: The Case of Korea. Review of Economics and Statistics 63:
520-525.
Allen, J. C. and D. F. Barnes 1985. The causes of deforestation in developing
countries. Annals of the Association of American Geographers 75: 163-184.
Angelsen, A. 1996. Deforestation: Population of Market Driven? Different Approaches in
Modelling of Agricultural Expansion. Working Paper # 9. Chr. Michelsen Institute, Bergen
Norway.
Barbier, E. and J. C. Burgess. 1996. Economic Analysis of Deforestation in Mexico.
Environment and Development Economics 1: 203-239.
Barnum, H. and L. Squire 1979. A Model of an Agricultural Household. Washington
D. C.: World Bank
Becker, G. 1965. A Theory of the Allocation of Time. Economic Journal 75:
493-517.
Binswanger, H. 1980. Attitudes toward Risk: Experimental Measurement in Rural India. American
Journal of Agricultural Economics 62: 395-407.
Binswanger, H. and J. McIntire. 1987. Behavioral and Material Determinants of
Production Relations in Land-abundant Tropical Agriculture. Economic Development and
Cultural Change 36: 73-99.
Blaikie, P. and H. C. Brookfield 1987. Land Degradation and Society. London:
Methuen.
Benjamin, D. 1992. Household Composition, Labor Markets, and Labor Demand: Testing for
Separation in Agricultural Household Models. Econometrica 60: 287-322.
Boserup, E. 1965. The Conditions of Agricultural Growth. Chicago: Aldine
Publishing Company.
Burgess, J. C. 1991. Economic analyses of frontier agricultural expansion and tropical
deforestation. MSc thesis. Environmental and Resource Economics, University College
London.
Capistrano, A. D. 1994. Tropical forest depletion and the changing macroeconomy,
1967-85. In Brown, K. and D. Pierce, eds. 1994. The Causes of Tropical Deforestation:
The economic and statistical analysis of factors giving rise to the loss of tropical
forests. London: UCL Press Limited.
Consultative Group on International Agricultural Research. 1996. (Report cited in New
York Times article: Report Blames Poor Farmers for Depleting World Forests, August 4,
1996).
Chayanov, A. V. 1926. Peasant farm organization. In D. Thorner, B Kerblay, and R. E. F.
Smith, eds. 1966. A. V. Chayanov in the Theory of the Peasant Economy. Homewood,
IL: Richard D. Irwin.
Chomnitz, K. M. and D. A. Gray. 1995. Roads, lands, markets, and deforestation: A
spatial model of land use in Belize. World Bank Policy Research Working Paper #1444.
Constantino, L. F. and D. Ingram. 1990. Supply-demand projections for the Indonesian
forestry sector. D. G. of Forest Utilization, Ministry of Forestry, Government of
Indonesia and FAO, Jakarta.
Cropper, M. and C. Griffiths. 1994. The Interaction of population Growth and
Environmental Quality. American Economics Review 84: 250-254.
Dalton, G. 1961. Economic theory and primitive society. American Anthropologist
62: 1-25.
De Janvry, A., M. Fafchamps, and E. Sadoulet. 1991. Peasant Household Behaviour with
Missing Markets: Some Paradoxes Explained. The Economic Journal 101: 1400-1417.
De Janvry, A, E. Sadoulet, B. Davis, G. Gordillo de Anda. 1996. Ejido Sector Reforms:
From Land Reform to Rural Development. In L Randall, ed. 1996. Reforming Mexico’s
Agrarian Reform. Armonk, New York: M.E. Sharpe.
Deacon, R. 1994. Deforestation and the Rule of Law in a Cross-Section of Countries. Land
Economics 70: 414-430.
Deininger, K. and B. Minten. 1996. Poverty, Politics, and Deforestation: The Case of
Mexico. Research project on the Social and Environmental Consequences of Growth-Oriented
Policies, Working Paper No. 5, Policy research Department, Washington D. C.: World Bank.
Didia, D. 1995. Developing Countries, Economic Interactions and Tropical Deforestation.
Dissertation, Department of Business Administration and Economics, State University of New
York, Brockport.
Dillon, J. and P. Scandizzo. 1978. Risk Attitudes of Subsistence Farmers in Northeast
Brazil. American Journal of Agricultural Economics 60: 425-435.
Dvorak, K. 1992. Resource Management by West African Farmers and the Economics of
Shifting Cultivation. American Journal of Agricultural Economics 74: 809-815.
Ewell, P. and D. Merrill-Sands. 1987. Milpa in Yucatan: A Long-Fallow Maize System and
Its Alternatives in the Maya Peasant Economy. In Turner II, B. L. and S. B. Brush, eds.
1987. Comparative Farming Systems. New York: The Guilford Press.
Foley, M. W. 1995. Privatizing the Countryside: The Mexican Peasant Movement and
Neoliberal Reform. Latin American Perspectives 22: 59-76.
Gates, M. 1988. Institutionalizing Dependency: The Impact of Two Decades of Planned
Agricultural Modernization on Peasants in the Mexican State of Campeche. The Journal of
Developing Areas 22: 293-320.
Geoghegan, J. and N. Bockstael. 1996. Ecological Economics, Geographic Information
Systems and Spatial Econometrics: Hedonic Models of the Patuxent Watershed. Department of
Agricultural and Resource Economics, University of Maryland, College Park.
Greene, W. (1993). Econometric Analysis, New York: Macmillan Publishing Company.
Grindle, M. 1984. Rhetoric, Reality, and Self-Sufficiency: Recent Initiatives in
Mexican Rural Development. Land Policy in Developing Countries. Lincoln Institute
Monograph #84-4: 45-53.
Grindle, M. 1989. The Response to Austerity: Political and Economic Strategies of
Mexico’s Rural Poor. In W. L. Canak, ed. 1989. Lost Promises: Debt, Austerity, and
Development in Latin America. Boulder: Westview Press.
Hammer, J. 1986. Subsistence First: Farm Allocation Decisions in Senegal. Journal of
Development Economics 23: 355-369.
Houghton, R. A. 1994. The Worldwide Extent of Land-use Change. BioScience 44:
305-313.
IGBP-HDP. 1995. Land-Use and Land-Cover Change Science/Research Plan.
Katila, M. 1992. Modelling deforestation in Thailand: the causes of deforestation
and deforestation projections for 1991-2010. Unpublished paper, Finnish Forestry
Institute, Helsinki.
Kaimowitz, D. and A. Angelsen. 1997. A Guide to Economic Models of Tropical
Deforestation. Draft Manuscript. Centre for International forestry Research, Jakarta,
Indonesia.
Katzman, M. 1975. The Brazilian Frontier in Comparative Perspective. Comparative
Studies in Society and History 17: 266-285.
Kiefer, N. (1988). Economic Duration Data and Hazard Functions. Journal of Economic
Literature, 26, 646-679.
Kummer, D. and Chi Ho Sham. 1994. The Causes of Tropical Deforestation: A Quantitative
Analysis and Case Study from the Philippines. In Brown, K. and D. Pierce, eds. 1994. The
Causes of Tropical Deforestation: The economic and statistical analysis of factors giving
rise to the loss of tropical forests. London: UCL Press Limited.
Kummer, D. and B. L. Turner II. 1994. The Human Causes of Deforestation in Southeast
Asia. BioScience 44: 323-328.
Lambin, E. F. 1994. Modelling Deforestation Processes. Trees Series B: Research Report
No. 1. Brussels, Luxembourg: ECSC-EC-EAEC.
Lipton, M. 1968. The Theory of the Optimizing Peasant. Journal of Development
Studies 4: 327-351.
Lopez, R. E. 1986. Structural Models of the Farm Household That Allow for
Interdependent Utility and Profit-Maximization Decisions. In Singh, I., L. Squire, J.
Strauss, eds. 1986. Agricultural Household Models: Extensions, Applications, and Policy.
Baltimore: The Johns Hopkins University Press.
McNeill, J., A., D. Alves, L. Arzipe, O. Bykova, K. Galvin, J. Kelmelis, S.
Migot-Adholla, P. Morrisette, R. Moss, J. Richards, W. Riebsame, F. Sadowski, S.
Sanderson, D. Skole, J. Tarr, M. Williams, S. Yadav, S. Young. 1994. Toward a Typology and
Regionalization of Land-Cover and Land-Use Change: Report of Working Group B. In Meyer,
W.B. and B.L. Turner II, eds. 1994. Land-Use and Land-Cover: A Global Perspective.
Cambridge: University of Cambridge Press.
Mertens, B. and E. F. Lambin. 1997. Spatial modelling of deforestation in southern
Cameroon. Applied Geography 17: 143-162.
Millar, J. R. 1970. A Reformulation of A. V. Chayanov’s Theory of the Peasant
Economy. Economic Development and Cultural Change 18: 219-229.
Moscardi, E. and A. de Janvry. 1977. Attitudes toward Risk among Peasants: An
Econometric Approach. American Journal of Agricultural Economics 59: 710-716.
Myers, N. 1991. The World’s Forests and Human Populations: The Environmental
Interconnections. In Davis, K. and M. S. Bernstam, eds. Resources, Environment, and
Population: Present Knowledge, Future Options. Population and Development Review, A
Supplement to Volume 16, 1990. New York: Oxford University Press.
Nakajima, C. 1969. Subsistence and Commercial Family Farms: Some Theoretical Models of
Subjective Equilibrium. In C. Wharton, ed. 1969. Subsistence Agriculture and Economic
Development. Chicago: Aldine Publishing Company.
Nelson, G. C. and D. Hellerstein. 1995. Do roads cause deforestation? using satellite
images in econometric analysis of land use. Staff Paper 95 E-448, Department of
Agricultural Economics. University of Illinois, Urbana-Champaign.
Lancaster, T. (1990). The Econometric Analysis of Transition Data. Cambridge:
Cambridge University Press.
Lombardini, C. 1994. Deforestation in Thailand. . In Brown, K. and D. Pierce, eds.
1994. The Causes of Tropical Deforestation: The economic and statistical analysis of
factors giving rise to the loss of tropical forests. London: UCL Press Limited.
Lugo, A. E., R. Schmidt, S. Brown 1981. Tropical forests in the Caribbean. Ambio
10: 318-324.
Osgood, D. 1994. Government failure and deforestation in Indonesia. . In Brown, K. and
D. Pierce, eds. 1994. The Causes of Tropical Deforestation: The economic and
statistical analysis of factors giving rise to the loss of tropical forests. London:
UCL Press Limited.
Palo, M, G. Mery, and J. Salmi. 1987. Deforestation in the Tropics: pilot scenarios
based on quantitative analyses. In Deforestation or Development in the Third World?
Vol. I, M. Palo and J. Salmi, eds. Helsinki: Metsantutkimuslaitoksen Tiedonantoja
(Research Bulletins of the Finnish Forestry Institute).
Panayotou, T. and S. Sungsuwan. 1989. An econometric study of the causes of tropical
deforestation: the case of Northeast Thailand. Discussion Paper No. 284, Harvard Institute
of International Development. Harvard University, Cambridge, MA.
Pellegrini, P. and S. Reader. (1996). Duration Modeling of Spatial Point Patterns. Geographic
Analysis, 28, 219-243.
Pfaff, A. S. P. 1996. "What drives deforestation in the Brazilian Amazon? evidence
from satellite and socioeconomic data." Draft Manuscript, Department of Economics,
Columbia University, June 1996.
Polanyi, K. 1944. The Great Transformation. New York: Holt, Rinehart, and
Winston, Inc.
Rayner, S., F. Bretherton, S. Buol, M. Fosberg, W. Grossman, R. Houghton, R. Lal, J.
Lee, S. Lonergan, J. Olson, R. Rockwell, C. Sage, and E. van Inhoff. 1994. A Wiring
Diagram for the Study of Land-Use/Cover Change: Report of Working Group A. In Meyer, W. B.
and B. L. Turner II, eds. 1994. Land-Use and Land Cover: A Global Perspective.
Cambridge: University of Cambridge Press.
Reis, E., and R. Guzman. 1994. An econometric model of Amazon deforestation. In Brown,
K. and D. Pierce, eds. 1994. The Causes of Tropical Deforestation: The economic and
statistical analysis of factors giving rise to the loss of tropical forests. London:
UCL Press Limited.
Rock, M. 1996. The Stork, The Plow, Rural Social Structure, and Tropical Deforestation
in Poor Countries? Ecological Economics 18: 113-131.
Roe, T. and T. Graham-Tomasi. 1986. Yield Risk in a Dynamic Model of the Agricultural
Household. In Singh, I., L. Squire, J. Strauss, eds. 1986. Agricultural Household
Models: Extensions, Applications, and Policy. Baltimore: The Johns Hopkins University
Press.
Rudel, T. 1989. Population, development, and deforestation: a cross-national study. Rural
Sociology 54: 327-338.
Sadoulet, E. and A. de Janvry. 1995. Quantitative Development Policy Analysis.
Baltimore: The Johns Hopkins University Press.
Sadoulet, E., A. de Janvry, and C. Benjamin. 1996. Household Behavior with Imperfect
Labor Markets. Working Paper #786. Department of Agricultural and Resource Economics,
Division of Agriculture and Natural Resources, University of California at Berkeley
Saha, A. 1994. A two-season agricultural household model of output and price
uncertainty. Journal of Development Economics 45: 245-269.
Shafik, N. 1994. Macroeconomic causes of deforestation: barking up the wrong tree? In
Brown, K. and D. Pierce, eds. 1994. The Causes of Tropical Deforestation: The economic
and statistical analysis of factors giving rise to the loss of tropical forests.
London: UCL Press Limited.
Southgate, D. 1994. Tropical Deforestation and agricultural development in Latin
America. In Brown, K. and D. Pierce, eds. 1994. The Causes of Tropical Deforestation:
The economic and statistical analysis of factors giving rise to the loss of tropical
forests. London: UCL Press Limited.
Thompson, G. and P. Wilson. 1994. Ejido Reforms in Mexico: Conceptual Issues and
Potential Outcomes. Land Economics 70: 448-465.
Walker, T. S. and J. G. Ryan. 1990. Village and Household Economies in India’s
Semi-Arid Tropics. Baltimore: Johns Hopkins University Press.
Warwick, D. P. and C. A. Luinger. 1975. The Sample Survey: Theory and Practice.
New York: McGraw Hill, Inc.
Salinas de Gortari, C. 1992. Iniciativa del Presidente Salinas (read before a Plenary
Session of the Chamber of deputies, November 7, 1991), pp. 75-94 in E. Valle Espinosa
(ed.) El Nuevo Art. 27: Cuestiones agrarias de Venustiano Carranza a Carlos Salinas.
Mexico City: Editorial Nuestra.
Sanderson, S. 1986. The Transformation of Mexican Agriculture: International
Structure and the Politics of Rural Change. Princeton: Princeton University Press.
Schultz, T. W. 1964. Transforming traditional agriculture. New Haven: Yale
University Press.
Sierra, L., L. Hernandez, and A. Hoy. 1992. La Zona Sur: Frontera Y Cambio Estructural
1970-1990.
Singh, I., L. Squire, J. Strauss, eds. 1986. Agricultural Household Models:
Extensions, Applications, and Policy. Baltimore: The Johns Hopkins University Press.
Stomph, T. J., L. O. Fresco, and H. van Keulen. 1994. Land Use System Evaluation:
Concepts and Methodology. Agricultural Systems 44: 243-255.
Turner, B. L. II, W. C. Clark, R. W. Kates, J. T. Richards, J. T. Mathews, and W. B.
Meyer, eds. 1990. The Earth as Transformed by Human Action. Cambridge University
Press, New York.
Walker, T. and N. Jodha. 1985 How Small Farm Households Adapt to Risk. In Hazell, P.,
C. Pomareda, and A. Valdes, eds. Agricultural Risks and Insurance: Issues in Policy.
Baltimore: Johns Hopkins University Press.
Wood, C. H., D. Skole, S. Perz and A. Caetano. 1996. Population and Deforestation in
the Brazilian Amazon. Paper presented at the 1996 Annual Meeting of the Population
Association of America, May 9-11, New Orleans.
Wharton, C. R. Jr., ed. 1969. Subsistence Agriculture and Economic Development.
Chicago: Aldine Publishing Company.
